Well, if we're counting Disney's Davy Crockett as a "western" TV show, I guess Dan'l Boone would count too. But the song I remember was
"Daniel Boone was the daddy of them all,
Was the daddy of them all,
Was the daddy of them all,
Daniel Boone heard the western forests call,
From the mountains to the Ohio!"

DK if that was the theme song from the TV show, though. Maybe just a pop spin-off from the hit "Ballad Of Davy Crockett" song from the Disney TV show.